The field of the invention is magnetic resonance imaging (MRI) and particularly, methods for acquiring and reconstructing diffusion weighted images.
Magnetic resonance imaging uses the nuclear magnetic resonance (NMR) phenomenon to produce images. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins, and after the excitation signal B1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx Gy and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. Each measurement is referred to in the art as a “view” and the number of views determines the quality of the image. The resulting set of received NMR signals, or views, or k-space samples, are digitized and processed to reconstruct the image using one of many well known reconstruction techniques. The total scan time is determined in part by the length of each measurement cycle, or “pulse sequence”, and in part by the number of measurement cycles, or “views,” that are acquired for an image. There are many clinical applications where total scan time for an image of prescribed resolution and SNR is a premium, and as a result, many improvements have been made with the objective of reducing scan time.
Recent work directed towards reducing total scan time includes using projection reconstruction methods as disclosed in U.S. Pat. No. 6,487,435. Projection reconstruction methods have been known since the inception of magnetic resonance imaging. Rather than sampling k-space in a rectilinear, or Cartesian, scan pattern as is done in Fourier imaging and shown in FIG. 2, projection reconstruction methods sample k-space with a series of views that sample radial lines extending outward from the center of k-space as shown in FIG. 3. The number of views needed to sample k-space determines the length of the scan and if an insufficient number of views are acquired, streak artifacts are produced in the reconstructed image. The technique disclosed in U.S. Pat. No. 6,487,435 is one method for reducing such streaking by acquiring successive undersampled images with interleaved views and sharing peripheral k-space data between successive image frames.
There are two methods used to reconstruct images from an acquired set of projection views as described, for example, in U.S. Pat. No. 6,710,686. In MRI the most common method is to regrid the k-space samples acquired on their radial sampling trajectories to a Cartesian grid. The image is then reconstructed by performing a 2D or 3D Fourier transformation of the regridded k-space samples. The second method for reconstructing an MR image is to transform the radial k-space projection views to Radon space by first Fourier transforming each projection view. An image is reconstructed from these signal projections by filtering and backprojecting them into the field of view (FOV) as is commonly done with x-ray CT data. As is well known in the art, if the acquired signal projections are insufficient in number to satisfy the Nyquist sampling theorem, streak artifacts are produced in the reconstructed image.
The standard backprojection method used in MRI is shown in FIG. 4. Each acquired signal projection profile 10 is backprojected onto the field of view 12 by projecting each signal sample 14 in the profile 10 through the FOV 12 along the projection path as indicted by arrows 16. In projecting each signal sample 14 in the FOV 12 we have no a priori knowledge of the subject being imaged and the assumption is made that the NMR signals in the FOV 12 are homogeneous and that the signal sample 14 should be distributed equally in each pixel through which the projection path passes. For example, a projection path 8 is illustrated in FIG. 3 for a single signal sample 14 in one signal projection profile 10 as it passes through N pixels in the FOV 12. The signal value (P) of this signal sample 14 is divided up equally between these N pixels:Sn=(P×1)/N  (1)
where: Sn is the signal value distributed to the nth pixel in a projection path having N pixels.
Clearly, the assumption that the backprojected signal in the FOV 12 is homogeneous is not correct. However, as is well known in the art, if certain corrections are made to each signal profile 10 and a sufficient number of profiles are acquired at a corresponding number of projection angles, the errors caused by this faulty assumption are minimized and image artifacts are suppressed. In a typical, filtered backprojection method of image reconstruction, 400 projections are required for a 256×256 pixel 2D image and 203,000 projections are required for a 256×256×256 voxel 3D image. If the method described in the above-cited U.S. Pat. No. 6,487,435 is employed, the number of projection views needed for these same images can be reduced to 100 (2D) and 2000 (3D).
Nerve tissue in human beings and other mammals includes neurons with elongated axonal portions arranged to form neural fibers or fiber bundles along which electrochemical signals are transmitted. In the brain, for example, functional areas defined by very high neural densities are typically linked by structurally complex neural networks of axonal fiber bundles. The axonal fiber bundles and other fibrous material are substantially surrounded by other tissue.
Diagnosis of neural diseases, planning for brain surgery, and other neurologically related clinical activities as well as research activities on brain functioning can benefit from non-invasive imaging and tracking of the axonal fibers and fiber bundles. In particular, diffusion tensor magnetic resonance imaging (DT-MRI) such as that disclosed in U.S. Pat. Nos. 6,526,305; 6,642,7126 and 6,806,705 has been shown to provide image contrast that correlates with axonal fiber bundles.
In the DT-MRI technique, motion sensitizing magnetic field gradients are applied in a so-called diffusion weighted imaging (DWI) pulse sequence so that the magnetic resonance images include contrast related to the diffusion of water or other fluid molecules. By applying the diffusion gradients in selected directions during the MRI measurement cycle, diffusion weighted images are acquired from which apparent diffusion tensor coefficients are obtained for each voxel location in the reconstructed image. Fluid molecules diffuse more readily along the direction of the axonal fiber bundle as compared with directions partially or totally orthogonal to the fibers. Hence, the directionality and anisotropy of the apparent diffusion coefficients tend to correlate with the direction of the axonal fibers and fiber bundles. Using iterative tracking methods, axonal fibers or fiber bundles can be tracked or segmented using the DT-MRI data.
However, to calculate the apparent diffusion tensor coefficients, it is necessary to acquire at least six DWI images using motion-sensitizing gradients directed in six different directions. Indeed, it is desirable to acquire more than six directions, but the acquisition of additional DWI images extends the total scan time beyond what is already a lengthy scan.